Structured variable selection prior. Our aim is to identify genomic markers associated with the PC scores, which translates to identifying the nonzero coefficients \(B^{(t)}\)  in the model in Equation (REF ). The genomic markers could themselves be correlated or have an inherent dependence structure (e.g. similar biological function or signaling pathway). We incorporate this information within the variable selection framework by proposing a generalization of structured continuous spike-and-slab priors as follows [1]}, [2]}:
\(\beta _{kj}^{(t,m)} \Big | \zeta _k^{(t,m)}, {\nu ^2_{kj}}^{(t,m)} & \stackrel{ind}{\sim } & N\big (0, \big [(1-\zeta _k^{(t,m)})v_0 + \zeta _k^{(t,m)}v_1\big ]{\nu ^2_{kj}}^{(t,m)}\big ) ~~\forall ~ k,j,t,m, \nonumber \\\zeta _k^{(t,m)} \Big | \lambda _k^{(t,m)} & \stackrel{ind}{\sim } & Ber(\Phi (\lambda _k^{(t,m)})) ~~\forall ~ k,t,m,  \\\mbox{$\lambda $}^{(t,m)} & \stackrel{ind}{\sim } & N(\mbox{$\mu $}^{(t,m)}, \Lambda ) ~~\forall ~ t,m, \nonumber \) 
